یحیی طالبی

Let R be a commutative semiring with nonzero identity and H be a multiplicative-prime subset of R. The generalized total graph of a commutative semir- ing R is the (undirected) graph GTH ( R) whose vertices are all elements of R and two distinct vertices x and y are adjacent if and only if x + y ∈ H . In this paper, we investigate the structure of GTH ( R) and we also study the two (induced) subgraphs GTH ( H ) and GTH ( R\H ) with vertex-sets H and R\H .